Abstract: We present measurements of partial branching fractions of B -> K+ X, B -> (KX)-X-0, and B -> pi(+) X, where X denotes any accessible final state above the endpoint for B decays to charmed mesons, specifically for momenta of the candidate hadron greater than 2.34 (2.36) GeV for kaons (pions) in the B rest frame. These measurements are sensitive to potential new-physics particles which could enter the b -> s(d) loop transitions. The analysis is performed on a data sample consisting of 383 X 10(6)B (B) over bar pairs collected with the BABAR detector at the PEP-II e(+)e(-) asymmetric energy collider. We observe the inclusive B -> pi(+) X process, and we set upper limits for B -> K+ X and B -> (KX)-X-0. Our results for these inclusive branching fractions are consistent with those of known exclusive modes, and exclude large enhancements due to sources of new physics.